Techniques for Constructing Complex Analytic Wavelets

Investigators

Staff:

David Tay.

Student: Van Nguyen.

Collaborations

N.G. Kingsbury, University of Cambridge, UK.

Description

Introduction: Wavelet analysis is one of the success stories in mathematics that has found many real world applications and some have been adopted by industry, eg. JPEG2000, digital cinema. Wavelet basis functions are excellent tools for analysing function space (eg. Sobolev) and signals (eg. image).

Significance: Traditional wavelets (eg. Daubechies family) are real valued. This project will develop techniques for constructing new wavelets that are complex valued. Complex wavelets can perform better in signal analysis as they provide angle or phase information not available from real wavelets.